Dividing is the process of splitting a number into equal parts or groups. It is the opposite operation of multiplication. When dividing, we are trying to determine how many times one number (the divisor) can be subtracted from another number (the dividend) without resulting in a negative number.

- Set up the division problem with the dividend inside the division symbol and the divisor outside the symbol. For example:
`25 ÷ 5`

- Start dividing the leftmost digit of the dividend by the divisor. If the divisor is greater than the first digit, continue to the next digit until a number greater than the divisor is found.
- Write the quotient above the line and the remainder, if any, next to the dividend.
- If there are more digits in the dividend, bring down the next digit and continue the process until the entire dividend is divided.

Long division is a method used for dividing multi-digit numbers. It involves a series of steps to find the quotient and remainder.

division-example.png" alt="Long Division Example">- Dividend: The number being divided.
- Divisor: The number that divides the dividend.
- Quotient: The result of the division.
- Remainder: The amount left over when the division is not exact.

Let's practice some division problems:

It's important to remember these rules when dividing:

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.